Question

Two capacitors of capacitances \(6\,\mu F\) and \(3\,\mu F\) are connected in series across a battery. The equivalent capacitance of the combination is

• A. \(9\,\mu F\)
• B. \(2\,\mu F\)
• C. \(4.5\,\mu F\)
• D. \(18\,\mu F\)

Hint:

Capacitors in series: \[ \boxed{\frac{1}{C_{\text{eq}}} = \frac{1}{C_1} + \frac{1}{C_2}} \] Capacitors in parallel: \[ \boxed{C_{\text{eq}}=C_1+C_2} \] Remember: \[ \boxed{\text{Series} \Rightarrow \text{Capacitance decreases}} \] \[ \boxed{\text{Parallel} \Rightarrow \text{Capacitance increases}} \]

Answer 1

The Correct Option is B

Step 1: Recall the formula for capacitors in series. \[ \frac{1}{C_{\text{eq}}} = \frac{1}{C_1} + \frac{1}{C_2} \] Given: \[ C_1=6\,\mu F \] \[ C_2=3\,\mu F \]

Step 2: Substitute the values. \[ \frac{1}{C_{\text{eq}}} = \frac{1}{6} + \frac{1}{3} \] \[ \frac{1}{C_{\text{eq}}} = \frac{1}{6} + \frac{2}{6} \] \[ \frac{1}{C_{\text{eq}}} = \frac{3}{6} = \frac{1}{2} \] \[ C_{\text{eq}} = 2\,\mu F \]

Step 3: Identify the correct option. \[ \boxed{C_{\text{eq}}=2\,\mu F} \] Therefore, \[ \boxed{\text{(B)}} \] is the correct answer.